Geodesic
On the theorems of Beurling, Carleson and Tsuji on exceptional sets
Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 1-12

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This paper consists of two parts. In the first part, a general theorem is proved on the behavior along chords of functions defined on the unit disk, and this theorem is applied to continuous functions of bounded type. In the second part, boundary uniqueness theorems are proved for functions meromorphic in the unit disk. Bibliography: 12 titles. 
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V. I. Gavrilov. On the theorems of Beurling, Carleson and Tsuji on exceptional sets. Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/SM_1974_23_1_a0/